Reading layer `israel_borders' from data source
`/cloud/project/israel/israel_borders.shp' using driver `ESRI Shapefile'
Simple feature collection with 1 feature and 1 field
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 615964.7 ymin: 3262612 xmax: 770622.2 ymax: 3691819
Projected CRS: WGS 84 / UTM zone 36N
mean median sd min max IQR
1 498.497 527.6 168.0896 24 956.6 177.1
[1] "This area got the most annual rainfall: Horashim"
[1] "This area got the least annual rainfall: Eilat"
The summary statistics for annual rainfall (in centimeters) and the histogram of the annual rainfall indicate a mean of approximately 498.50 cm and a median of 527.60 cm, suggesting a left-skewed distribution influenced by lower rainfall years. The standard deviation of 168.09 cm reflects significant variability, highlighting the potential for both drought and excessive rainfall. The data range from a minimum of 24 cm to a maximum of 956.60 cm, illustrating the extremes in weather patterns. The interquartile range (IQR) of 177.10 cm signifies notable variation in typical annual rainfall.
The color gradient indicates the amount of rainfall, with darker shades representing higher precipitation and lighter shades indicating lower rainfall. Based on the map, it appears that:Northern area receives the highest amount of rainfall, with a significant portion of the region receiving over 750 cm of annual rainfall. Southern area experiences considerably lower rainfall, with many areas receiving less than 250 cm per year. The coastal region receives moderate rainfall, with annual precipitation typically ranging between 250 and 500 cm.
[inverse distance weighted interpolation]
The IDW interpolation with a power of 0 is very smooth and gives the mean annual rainfall for all areas
[inverse distance weighted interpolation]
the IDW interpolation with a power of 1 offers a more informative representation of the predicted annual rainfall than power zero which shows that all areas have the same amount of annual rainfall. The map shows most of the areas received an annual rainfall above 300cm. The map though smooth reveals gradual changes in rainfall intensity across the region, with gradients from wetter areas in the north to drier areas in the south.
[inverse distance weighted interpolation]
The IDW interpolation with a power of 2 exhibits less smoothness and reveals distinct trends compared to the interpolation with power 1. In the southern region, areas now appear darker, indicating annual rainfall levels below 200 cm, which suggests a decrease in rainfall compared to the power 1 interpolation. While the northern areas continue to receive more rainfall, the amounts are still lower than those predicted with power 1. Notably, the regions experiencing the highest annual rainfall are concentrated in the north westernmost areas which agrees with the orginal data as the points in those areas were very light. The tip of the south gets less more than 400cm annual rainfall rain than the tip of the north
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
IDW..power...0. IDW..power...1. IDW..power...2.
1 166.3445 127.5178 85.0365
The IDW results for the different power coefficients show distinct variations in estimated annual rainfall. For a power of 0, the average rainfall estimate is 166.34 cm, which indicates that the interpolation is uniform across the area, treating all points equally without considering their distance. As the power increases to 1, the average estimate drops to 127.52 cm, reflecting a moderate weighting of nearby points over those further away. Finally, at a power of 2, the average estimate further decreases to 85.04 cm, suggesting that the interpolation is heavily influenced by the nearest points, resulting in a more localized and potentially less smooth surface.
[inverse distance weighted interpolation]
The points along the line are shaded darker, indicating they are farther from a residual of zero. Additionally, many points are located well above and below the line, suggesting the model tends to underestimate higher rainfall values and overestimate lower ones. This highlights areas where the model’s predictions diverge significantly from the actual data.
[inverse distance weighted interpolation]
The points are mostly scattered around the diagonal line, indicating that the predicted annual rainfall values are generally close to the observed values.The color of the dots on the line indicates that the residual are close to zero which indicates that model predicts annual rainfall well.However, few points are located farther away from the diagonal line indicating larger differences between predicted and observed values.The residual range from -200 to 200 which is different from the range of the residuals of the model with power 0
[inverse distance weighted interpolation]
For the IDW interpolation with a power of 2, most points along the diagonal are shaded like the shades around zero, indicating that their residuals are close to zero, which suggests the model is performing well in predicting annual rainfall. However, there are a few points that deviate from the line. The lightly shaded points below the line indicate the model is underestimating rainfall in those areas, while the darker points above the line show overestimation. Most of these points are still very close to the diagonal, meaning the deviations are relatively small, overall reflecting a good model fit.The range for the residuals for this model is 100 points less than that of the model with power 0 and 1
[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]
RMSE
1 64.85976
RMSE= 64.9cm which is less than the RMSE of the IDW with different powers.
The analysis of annual rainfall across the region provided significant insights through the application of both IDW (Inverse Distance Weighting) and Kriging interpolation methods. The IDW method was applied with varying power coefficients (0, 1, and 2) to assess how spatial weighting affects rainfall estimation. Summary statistics showed that annual rainfall varied widely, with values ranging from a minimum of 24 cm to a maximum of 956.60 cm, indicating diverse climatic conditions within the area.
The IDW interpolation with a power of 0 resulted in a uniform rainfall estimate, failing to capture local variability, resulting in an RMSE of 166.34 cm. With power 1, the IDW method provided a less smooth map, revealing gradual spatial changes in annual rain, but still produced a higher RMSE of 127.52cm. Power 2 further highlighted distinctions between areas, particularly illustrating the stark contrast between the southern and northern regions of the study area(northern areas received more annual rainfall than the south did), yielding an RMSE of 85 cm. Thus the IDW with power 2, did a better job at predicting annual rainfall.
However, the cross-validation results highlighted the superior performance of the Kriging method in estimating rainfall. With the lowest RMSE of 64.9cm. Based on the Root Square Mean Error(RMSE), Kriging demonstrated a more accurate representation of spatial rainfall patterns compared to all IDW configurations. This method effectively accounts for both the distance and the spatial correlation between points, leading to improved predictions that are not only more precise but also better at capturing the underlying rainfall variability across the region.